102 lines
2.7 KiB
Markdown
102 lines
2.7 KiB
Markdown
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# Matrix4 / Matrix4x4
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4x4 矩阵结构体，用于表示完整的 3D 变换（平移、旋转、缩放）、视图和投影变换。
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## 头文件
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```cpp
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#include <XCEngine/Math/Matrix4.h>
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```
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## 命名空间
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`XCEngine::Math`
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## 类型别名
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```cpp
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using Matrix4 = Matrix4x4;
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```
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## 存储方式
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行优先存储 (row-major)：
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```
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m[0][0] m[0][1] m[0][2] m[0][3]
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m[1][0] m[1][1] m[1][2] m[1][3]
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m[2][0] m[2][1] m[2][2] m[2][3]
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m[3][0] m[3][1] m[3][2] m[3][3]
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```
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## 静态工厂方法
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### 基础变换
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `Identity()` | `Matrix4` | 单位矩阵 |
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| `Zero()` | `Matrix4` | 零矩阵 |
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| `Translation(const Vector3& v)` | `Matrix4` | 平移矩阵 |
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| `Scale(const Vector3& v)` | `Matrix4` | 缩放矩阵 |
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| `Rotation(const Quaternion& q)` | `Matrix4` | 旋转矩阵（四元数） |
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| `TRS(translation, rotation, scale)` | `Matrix4` | 完整变换 |
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### 旋转
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `RotationX(float radians)` | `Matrix4` | X 轴旋转 |
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| `RotationY(float radians)` | `Matrix4` | Y 轴旋转 |
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| `RotationZ(float radians)` | `Matrix4` | Z 轴旋转 |
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### 相机变换
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `LookAt(eye, target, up)` | `Matrix4` | 视图矩阵 |
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| `Perspective(fov, aspect, near, far)` | `Matrix4` | 透视投影 |
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| `Orthographic(left, right, bottom, top, near, far)` | `Matrix4` | 正交投影 |
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## 实例方法
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### 乘法
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `operator*(Matrix4, Matrix4)` | `Matrix4` | 矩阵乘法 |
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| `operator*(Matrix4, Vector4)` | `Vector4` | 矩阵-向量乘法 |
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| `MultiplyPoint(v)` | `Vector3` | 点变换（带平移） |
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| `MultiplyVector(v)` | `Vector3` | 方向变换（不带平移） |
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### 分解
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `Transpose()` | `Matrix4` | 转置矩阵 |
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| `Inverse()` | `Matrix4` | 逆矩阵 |
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| `Determinant()` | `float` | 行列式 |
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| `GetTranslation()` | `Vector3` | 获取平移分量 |
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| `GetRotation()` | `Quaternion` | 获取旋转分量 |
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| `GetScale()` | `Vector3` | 获取缩放分量 |
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| `Decompose(translation, rotation, scale)` | `void` | 分解所有分量 |
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## 使用示例
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```cpp
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// MVP 矩阵
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Matrix4 model = Matrix4::TRS(position, rotation, scale);
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Matrix4 view = Matrix4::LookAt(cameraPos, target, Vector3::Up());
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Matrix4 proj = Matrix4::Perspective(45.0f * DEG_TO_RAD, aspect, 0.1f, 100.0f);
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Matrix4 mvp = proj * view * model;
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// 变换点
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Vector3 worldPos = model.MultiplyPoint(localPos);
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Vector3 worldDir = model.MultiplyVector(localDir);
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// 分解矩阵
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Vector3 translation;
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Quaternion rotation;
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Vector3 scale;
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model.Decompose(translation, rotation, scale);
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```
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